Asymptotic solution for a class of impulsive differential equations
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摘要: 研究一类含有单个脉冲点的脉冲微分方程. 基于奇摄动理论, 通过分步法, 将原脉冲微分方程问题扩充为奇摄动问题, 证明了扩充问题的解是原问题解很好的近似, 从而为进一步研究脉冲微分方程问题提供了新途径. 其次, 利用边界层函数法, 构造了原问题连续的形式渐近解, 证明了解的存在性和进行了余项估计. 最后, 通过例子验证了主要结果.Abstract: By means of singular perturbation theory, We constructed the singularly perturbed problem for the impulsive differential equation problem, and proved that the solution of the derived problem approximated to the solution of original problem, indicating a new way for the study of impulsive differential equations. By virtue of boundary function method, we not only constructed continuous formal asymptotic solution but also proved the existence of solution, meanwhile the remainder estimate was presented. Finally, an example was given to illustrate the results.
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